Statistics and Probability Answers

Suppose you have a Simple population regression function describe as follows derive the ordinary least squares estimator of the coefficients.

You are a researcher who is interested in how watching television influences children’s performance in school. You find out how many hours of television 5 children watch, on average, in a week. You have obtained their overall grade average.

Child No. Hours of TV Overall Grade Average

1 5 80

2 20 67

3 6 75

4 14 70

5 12 80

a. Calculate the correlation between hours of television watched and overall grade average. Interpret the correlation – what does it mean?

b. Calculate the regression equation (use television watching to predict grade).

c. Make a scatter plot of the data and draw the line of best fit on your scatter plot.

Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of

compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the

treatments (cars types). Using the hypothetical data provided below, test whether the mean

pressure applied to the driver’s head during a crash test is equal for each types of car. Use α = 5%.

Compact cars Midsize cars Full-size cars

643 469 484

655 427 456

702 525 402

Mean 666.67 473.67 447.33

Standard 31.18 49.17 41.68

deviation

In a market survey conducted to examine whether the choice of a brand is related to the income levels of the consumers, a random sample of 400 consumers reveal the following:

Income level Brand 1 Brand 2 Brand 3 Total

per month

20000 93 72 75 240

20000-50000 50 35 37 122

>50000 12 15 11 38

Total 155 122 123 400

Test the association between income level and brand preference at 5% significant level.

Consider a population having a standard deviation equal to 10, we wish to estimate the

for a mean of this population with an error bound equal to 1?

ii.Suppose we take a random sample of size we have determined in part (i), if we

i.How large a random sample is needed to construct a 95.44% confidence interval

obtain a sample mean equal to 295, calculate the 95.44% confidence interval for

the population mean. What is the interval error bound?

A bank Manager developed a new System to reduce the time customers spend waiting for a teller

service during peak hours. The Manager hopes that the new system will reduce the waiting time

hypothesis and alternative hypothesis needed if we want to attempt to provide evidence

the 100 waiting times to support the claim that the mean waiting time under new system is shorter

than 6 minutes.

from the current 9 to 10 minutes to less than 6 minutes. Suppose that the Managerwishes to use

a)Letting µ represent the mean waiting time under the new system, set up the null

b)In the context of this situation interpret making a type I error, interpret making a type II error

supporting claim that µ is shorter than 6 minutes.